  Patterns of problems

## Oscillations

- It is always better to be prepared. Practice the kind of problems asked in various exams
1
Direct use of the equation of simple harmonic motion
In this type of problems, direct use of the equation of simple harmonic motion is the key. Suppose we have one equation of SHM in our hands. Now, if we compare this equation with the standard equation of SHM then we can easily find the amplitude, frequency etc. of that particular SHM. Let us see some examples.
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2
Finding frequency of oscillation from the expression of acceleration
The acceleration of a simple harmonic motion is related to the displacement with the equation . Therefore, if we can write an equation of this kind then we can directly find the angular frequency of oscillation. on the other hand, if we know angular frequency and displacement then we can find acceleration and then velocity by integration.
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3
Superposition of two collinear harmonic oscillations
When two collinear harmonic oscillations superimpose then the resultant displacement is the vector sum of two individual displacements. The resultant amplitude, frequency and phase will depend on the individual amplitudes, frequency and phase.
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4
Superposition of two perpendicular harmonic oscillations
When two perpendicular harmonic oscillations with equal frequencies superimpose, the resultant displacement is the vector sum of the individual displacements. But in this case, the resultant need not be a harmonic oscillation. The resultant motion can be rectilinear, elliptical, circular depending on the phase difference and amplitude of the constituents oscillations.
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5
Finding various parameters in an oscillating spring-mass system
A common example of a system that executes simple harmonic motion is a spring-mass system. Questions can be asked to calculate the time period of oscillation or angular frequency of oscillation etc. In this kind of problems, we first try to find the equivalent spring constant and then find the required parameters with the help of Hooke's law.
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6
Finding frequency or time period of systems executing simple harmonic motion
Apart from a spring-mass system, there are various other systems that execute simple harmonic motion. In most of the problems, we are asked to find the time period or frequency of such oscillations. Some common examples of this kind of systems are a torsional pendulum, vibrating liquid column in a U-tube, a floating object, an electrical system etc.
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7
Finding various parameters in a damped oscillation
A oscillation is said to be damped when its amplitude decreases continuously after every oscillation. The equation of displacement representing damped oscillation is quite different than that of a free oscillation. With the help of this equation, one can find the logarithmic decrement of amplitude, frequency of oscillation, total energy, energy dissipation etc.
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8
Calculating resonance frequency
One of the most intriguing concept associated with forced oscillation is the concept of resonance. At this resonance frequency the amplitude of vibration is maximum. questions can be asked in different ways to calculate the resonance frequency.
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